Question

$$9 ^ { x - 1 } = 3 ^ { 2 x - 1 } - 486 x$$

Answer

$$n=-(3^(2*x-1)-9^(x-1))/(486*e^3*IM*t^2*h^2*v*a*l*u*o*f*x*s)$$

Solution


Simplify  \(486thenthevalueofx\imath s-\)  to  \(486{e}^{3}\imath {t}^{2}{h}^{2}nvaluofxs-\).
\[{9}^{x-1}={3}^{2x-1}-486thenthevalueofx\imath s-\]
Simplify  \(486thenthevalueofx\imath s-\)  to  \(486{e}^{3}\imath {t}^{2}{h}^{2}nvaluofxs-\).
\[{9}^{x-1}={3}^{2x-1}-486thenthevalueofx\imath s-\]
Subtract \({3}^{2x-1}\) from both sides.
\[{9}^{x-1}-{3}^{2x-1}=-486thenthevalueofx\imath s-\]
Multiply both sides by \(-1\).
\[-{9}^{x-1}+{3}^{2x-1}=486thenthevalueofx\imath s-\]
Simplify  \(486thenthevalueofx\imath s-\)  to  \(486{e}^{3}\imath {t}^{2}{h}^{2}nvaluofxs-\).
\[-{9}^{x-1}+{3}^{2x-1}=486{e}^{3}\imath {t}^{2}{h}^{2}nvaluofxs-\]
Regroup terms.
\[-{9}^{x-1}+{3}^{2x-1}=-+486{e}^{3}\imath {t}^{2}{h}^{2}nvaluofxs\]
Regroup terms.
\[{3}^{2x-1}-{9}^{x-1}=-+486{e}^{3}\imath {t}^{2}{h}^{2}nvaluofxs\]
Simplify  \(+486{e}^{3}\imath {t}^{2}{h}^{2}nvaluofxs\)  to  \(486{e}^{3}\imath {t}^{2}{h}^{2}nvaluofxs\).
\[{3}^{2x-1}-{9}^{x-1}=-486{e}^{3}\imath {t}^{2}{h}^{2}nvaluofxs\]
Divide both sides by \(-486\).
\[-\frac{{3}^{2x-1}-{9}^{x-1}}{486}={e}^{3}\imath {t}^{2}{h}^{2}nvaluofxs\]
Divide both sides by \({e}^{3}\).
\[-\frac{\frac{{3}^{2x-1}-{9}^{x-1}}{486}}{{e}^{3}}=\imath {t}^{2}{h}^{2}nvaluofxs\]
Simplify  \(\frac{\frac{{3}^{2x-1}-{9}^{x-1}}{486}}{{e}^{3}}\)  to  \(\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}}\).
\[-\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}}=\imath {t}^{2}{h}^{2}nvaluofxs\]
Divide both sides by \(\imath \).
\[-\frac{\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}}}{\imath }={t}^{2}{h}^{2}nvaluofxs\]
Simplify  \(\frac{\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}}}{\imath }\)  to  \(\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath }\).
\[-\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath }={t}^{2}{h}^{2}nvaluofxs\]
Divide both sides by \({t}^{2}\).
\[-\frac{\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath }}{{t}^{2}}={h}^{2}nvaluofxs\]
Simplify  \(\frac{\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath }}{{t}^{2}}\)  to  \(\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath {t}^{2}}\).
\[-\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath {t}^{2}}={h}^{2}nvaluofxs\]
Divide both sides by \({h}^{2}\).
\[-\frac{\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath {t}^{2}}}{{h}^{2}}=nvaluofxs\]
Simplify  \(\frac{\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath {t}^{2}}}{{h}^{2}}\)  to  \(\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath {t}^{2}{h}^{2}}\).
\[-\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath {t}^{2}{h}^{2}}=nvaluofxs\]
Divide both sides by \(v\).
\[-\frac{\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath {t}^{2}{h}^{2}}}{v}=naluofxs\]
Simplify  \(\frac{\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath {t}^{2}{h}^{2}}}{v}\)  to  \(\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath {t}^{2}{h}^{2}v}\).
\[-\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath {t}^{2}{h}^{2}v}=naluofxs\]
Divide both sides by \(a\).
\[-\frac{\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath {t}^{2}{h}^{2}v}}{a}=nluofxs\]
Simplify  \(\frac{\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath {t}^{2}{h}^{2}v}}{a}\)  to  \(\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath {t}^{2}{h}^{2}va}\).
\[-\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath {t}^{2}{h}^{2}va}=nluofxs\]
Divide both sides by \(l\).
\[-\frac{\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath {t}^{2}{h}^{2}va}}{l}=nuofxs\]
Simplify  \(\frac{\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath {t}^{2}{h}^{2}va}}{l}\)  to  \(\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath {t}^{2}{h}^{2}val}\).
\[-\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath {t}^{2}{h}^{2}val}=nuofxs\]
Divide both sides by \(u\).
\[-\frac{\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath {t}^{2}{h}^{2}val}}{u}=nofxs\]
Simplify  \(\frac{\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath {t}^{2}{h}^{2}val}}{u}\)  to  \(\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath {t}^{2}{h}^{2}valu}\).
\[-\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath {t}^{2}{h}^{2}valu}=nofxs\]
Divide both sides by \(o\).
\[-\frac{\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath {t}^{2}{h}^{2}valu}}{o}=nfxs\]
Simplify  \(\frac{\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath {t}^{2}{h}^{2}valu}}{o}\)  to  \(\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath {t}^{2}{h}^{2}valuo}\).
\[-\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath {t}^{2}{h}^{2}valuo}=nfxs\]
Divide both sides by \(f\).
\[-\frac{\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath {t}^{2}{h}^{2}valuo}}{f}=nxs\]
Simplify  \(\frac{\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath {t}^{2}{h}^{2}valuo}}{f}\)  to  \(\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath {t}^{2}{h}^{2}valuof}\).
\[-\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath {t}^{2}{h}^{2}valuof}=nxs\]
Divide both sides by \(x\).
\[-\frac{\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath {t}^{2}{h}^{2}valuof}}{x}=ns\]
Simplify  \(\frac{\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath {t}^{2}{h}^{2}valuof}}{x}\)  to  \(\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath {t}^{2}{h}^{2}valuofx}\).
\[-\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath {t}^{2}{h}^{2}valuofx}=ns\]
Divide both sides by \(s\).
\[-\frac{\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath {t}^{2}{h}^{2}valuofx}}{s}=n\]
Simplify  \(\frac{\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath {t}^{2}{h}^{2}valuofx}}{s}\)  to  \(\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath {t}^{2}{h}^{2}valuofxs}\).
\[-\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath {t}^{2}{h}^{2}valuofxs}=n\]
Switch sides.
\[n=-\frac{{3}^{2x-1}-{9}^{x-1}}{486{e}^{3}\imath {t}^{2}{h}^{2}valuofxs}\]